# TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY

TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png The Review of Symbolic Logic Cambridge University Press

# TRANSFINITE NUMBERS IN PARACONSISTENT SET THEORY

, Volume 3 (1): 22 – Jan 14, 2010
22 pages

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# References (28)

Publisher
Cambridge University Press
ISSN
1755-0211
eISSN
1755-0203
DOI
10.1017/S1755020309990281
Publisher site
See Article on Publisher Site

### Abstract

This paper begins an axiomatic development of naive set theory—the consequences of a full comprehension principle—in a paraconsistent logic. Results divide into two sorts. There is classical recapture, where the main theorems of ordinal and Peano arithmetic are proved, showing that naive set theory can provide a foundation for standard mathematics. Then there are major extensions, including proofs of the famous paradoxes and the axiom of choice (in the form of the well-ordering principle). At the end I indicate how later developments of cardinal numbers will lead to Cantor’s theorem, the existence of large cardinals, and a counterexample to the continuum hypothesis.

### Journal

The Review of Symbolic LogicCambridge University Press

Published: Jan 14, 2010